ABSTRACT ALGEBRA I

Instructors: Marlow Anderson (Palmer 133) & Josh Laison (Palmer 140).

Office Hours:  At least one of us will be available every afternoon 1:30-2:30; we’ll be around at other times too.

Text: Contemporary Abstract Algebra, by Joseph Gallian.

Class Time: We will meet each morning at 9 a.m.; there will be a class session 1-2:30 p.m. on Friday, December 6th.

Exams: There will be two take home exams. You will be allowed to consult your book and notes, but should not consult any other written source, or any person except one of the course instructors. The midterm will be due on Friday, December 6th, and the final exam on Thursday, December 19th. Each of these exams will count for 25% of your grade.

Quizzes: There will be 4 short quizzes, which are closed book, notes and colleagues.   We will make the quizzes available after class on the days they are scheduled; they are due by 2 p.m. that afternoon.  Each Quiz will count for 5% of your grade.

Homework: Most days we will assign a few hand-in homework problems, which are due the class day after they are assigned, by 3:30 p.m. Feel free to discuss these problems with your colleagues in class; however, your finished write-up of the problem should be your own. We will regularly expect you to present solutions to selected homework problems in class. Your Homework score (including credit for class participation) will account for 20% of your grade.

Project:  You will work in pairs in preparing a final project, presenting a further topic in abstract algebra not covered in class.  These projects might involve applications, history or extra mathematical topics. We will provide guidance for references, depending on your own interest.  Each pair will schedule an appointment with one of us before 1 p.m. on Tuesday, December 17th to discuss your project; you should by that time have significant progress to show us.  You and your partner will hand in one written essay (1000-1500 words), and in addition present your project orally to the class (20 to 30 minutes), on Thursday December 19th.  The project will count for the remaining 10% of your grade.

Links:  There are some nice Java Applet Exercises keyed to the chapters of our text.  These provide valuable practice and review, and you’re encouraged to try them out.  We’ll be happy to discuss them in class.  The link is http://www.d.umn.edu/~jgallian/msproject/project_head.html.

We will be making some use of a computer algebra system called GAP.  This program is available on the machines in the mathematics computer lab (Palmer 14).  You can download your own copy of GAP for free at

http://www.gap-system.org/Info4/distrib.html. 

You can also obtain a lab manual for GAP associated with our textbook at http://college.hmco.com/mathematics/gallian/abstract_algebra/5e/students/gap.html .  We will occasionally be assigning some GAP exercises from the lab manual and our text.  There are some subroutine files needed when using the manual, that you can copy either from the textbook website, or from the bin subdirectory on one of the machines in the lab downstairs.

 

 

Course Schedule

Date

Chapters

Topic

Mon. Nov. 25

0

Review of Number Theory

Tues. Nov. 26

1-2

Definition and Examples of Groups

Wed. Nov. 27

3-4

Subgroups and Cyclic groups; Quiz #1

Mon. Dec. 2

5

Permutation Groups

Tues. Dec. 3

6

Cayley’s Theorem

Wed. Dec. 4

7

Lagrange’s Theorem; Quiz #2

Thurs. Dec. 5

Review AM

Midterm handed out immediately after the review

Fri. Dec. 6

8

Midterm due at noon; Direct Products (1-2:30 p.m.)

Mon. Dec. 9

9

Normal Subgroups

Tues. Dec. 10

10

The Isomorphism Theorem

Wed. Dec. 11

12

Rings; Quiz #3

Thurs. Dec. 12

13

Integral Domains & Fields

Fri. Dec. 13

14-15

Ideals & Homomorphisms

Mon. Dec. 16

16

Polynomial Rings; Quiz #4

Tues. Dec. 17

Review AM

Final handed out immediately after review

Wed. Dec. 18

27

Simple Groups

Thurs. Dec. 19

 

Final due at 9 a.m.; Project Presentations

Wed. Dec. 25

Christmas